A MACHINE-ASSISTED PROOF OF GÖDEL’S INCOMPLETENESS THEOREMS FOR THE THEORY OF HEREDITARILY FINITE SETS
A MACHINE-ASSISTED PROOF OF GÖDEL’S INCOMPLETENESS THEOREMS FOR THE THEORY OF HEREDITARILY FINITE SETS
Lawrence Charles Paulson
TLDR
This is apparently the first mechanical verification of the second incompleteness theorem using the Isabelle proof assistant, which closely follows Świerczkowski (2003), who gave a detailed proof using hereditarily finite set theory.
Abstract
Abstract A formalization of Gödel’s incompleteness theorems using the Isabelle proof assistant is described. This is apparently the first mechanical verification of the second incompleteness theorem. The work closely follows Świerczkowski (2003), who gave a detailed proof using hereditarily finite set theory. The adoption of this theory is generally beneficial, but it poses certain technical issues that do not arise for Peano arithmetic. The formalization itself should be useful to logicians, particularly concerning the second incompleteness theorem, where existing proofs are lacking in detail.